is "make love not violence" grammatically correct or not?

There's a center in Russia that helps victims of sexual assault, and I bought a t-shirt from them with the slogan "make love not violence" but as I started to think about this phrase, it started to seem that it's a clear mistake because it's a mistake to use make instead of do with violence. However, some people think, as this phrase stems from "make love not war", it's possible to change last word to give this phrase a different meaning, and even though it's not grammatically perfect, it wouldn't be considered a real mistake. As I am not sure about that, I'd like to ask all real grammar pros here, please help us know if it's a mistake or not.

What baffled me is that when I searched in quotes on Google, it gave me little to no results in English. Second, I get when it can be used as on object like in the case "make violence great again", but here it seems that its goal was to be used in idiomatic case, but there's no such case. Please, correct me if I'm wrong.

It is grammatically correct. “Make violence” is a parseable English sentence, a transitive verb in the imperative case, followed by a noun as the direct object.

What it is not is idiomatic. Violence is not “made”, at least in American English. You can make love and you can make war but violence is “done”, “committed”, “perpetrated”, or even “instigated”.

Edit: Tim brings up an interesting case: “Make violence great again.”

This is actually idiomatic: even fo nouns for which “make [noun]” is not used, “make [noun adjective]” still often is.

For example, consider these sentences:

The statute made fraud illegal.

Bernie Madoff made fraud.

The first sentence is fine but the second just wrong (idiomatically wrong — it’s factually correct). As with “violence”, fraud is “committed”.

Strangely, you cannot “do” fraud, or most crimes, but you can “do murder”.